Issue |
ESAIM: M2AN
Volume 44, Number 4, July-August 2010
|
|
---|---|---|
Page(s) | 597 - 625 | |
DOI | https://doi.org/10.1051/m2an/2010021 | |
Published online | 17 March 2010 |
The G method for heterogeneous anisotropic diffusion on general meshes
1
IFP,
1 & 4 av. du Bois-Préau,
92852 Rueil-Malmaison Cedex, France.
leo.agelas@ifp.fr; daniele-antonio.di-pietro@ifp.fr
2
Université Montpellier 2,
Institut de Mathématiques et Modélisation de Montpellier,
CC 051,
Place Eugène Bataillon,
34095 Montpellier Cedex 05, France.
droniou@math.univ-montp2.fr
Received:
27
November
2008
In the present work we introduce a new family of cell-centered Finite
Volume schemes for anisotropic and heterogeneous diffusion operators
inspired by the MPFA L method.
A very general framework for the convergence study of finite volume
methods is provided and then used to establish the convergence of the
new method.
Fairly general meshes are covered and a computable sufficient
criterion for coercivity is provided.
In order to guarantee consistency in the presence of heterogeneous
diffusivity, we introduce a non-standard test space in
(Ω) and prove its density.
Thorough assessment on a set of anisotropic heterogeneous problems as
well as a comparison with classical multi-point Finite Volume methods
is provided.
Mathematics Subject Classification: 65N08 / 65N12
Key words: Finite volume methods / heterogeneous anisotropic diffusion / MPFA / convergence analysis
© EDP Sciences, SMAI, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.